In the mid-sixties, most countries standardized on ISO paper sizes (A-series, B-series, etc.). The Americas didn't. Why not?
(Around the same time there was a failed push in the US to switch to metric, but this seems like a different issue.)
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The whole range of ISO sizes uses the
1 / sqrt( 2 ) side ratio (1 : 1,414), with the base A0 size being defined as having an area of one square meter.
The constant side ratio
1 / sqrt(2) (1 : 1,414) was already mentioned by Lichtenberg (1786), and used during the French Revolution ("Loi sur le Timbre"). Reinvented with the "Weltformat" by Ostwald (1910), his assistant Porstmann came up with the square meter base sheet (A0) and the B series for envelopes (1922).
The German Wikipedia entry on "Paper sizes" has some of the criticisms voiced about this format. Quoting from there, translation mine:
Arguments against their [DIN / ISO sizes] introduction were, for example, that standardization was desirable, but the advantage of the constant side ratio remained unclear. If respecting the grain of the paper, two different sheets would have to be used as point of origin anyway. If using the same sheet, every other format would be across the grain.
The constant side ratio was considered unaesthetic, a "hybrid format" between the aforementioned formats 2:3 [for hand-held books] and 3:4 [for books to be put on a table top].
Also, the absolute size of the normal formats appeared arbitrary, as it was not being defined in terms of the "used" formats A4 and A5, but by defining the size of the A0 sheet as being one square meter. That multiple folding resulted in usable sizes was rather coincidental.
A disadvantage resulted from the A4 format being 17mm taller than the US Letter format, which was considered annoying when filing them in North American binders.
: Jan Tschichold: Willkürfreie Maßverhältnisse der Buchseite und des Satzspiegels, in: Ausgewählte Aufsätze über Fragen der Gestalt des Buches und der Typographie. Basel 1975, S. 50.
: Jan Tschichold: Erfreuliche Drucksachen durch gute Typographie. Augsburg 2001, S. 112–115.
The last point -- A4 not fitting into binders -- was less of an issue in Germany, where A4 did fit binders based on the Folio format (210 × 330mm) well enough.
A more likely reason than these technical issues, though, was the inertia of the North American market. Being far remote from Germany and the fractured European market (with its needs for standardization), and not having adopted the metric system either, it probably seemed easier all-around to stick with the existing inch-based formats.
In Germany alone three different basic sizes were used for letters -- Reichsformat (33x42cm), Super-Royal (50x68cm), and Groß Patria (36x43cm). People were facing problems with ill-fitting envelopes, binders, and boxes, so the pressure for standardization was there before even considering the formats used in neighboring countries.[source]